The newspaper claims that Johnson called Mordaunt and asked her to withdraw from the Tory leadership race and support his candidacy instead.
According to the publication, Johnson spoke to her by phone on the afternoon of Sunday, October 23.
Currently, the politician is trying to build a coalition before noon on Monday that will support him in the fight for the post of prime minister, the authors write.
After Liz Truss announced her resignation, Penny Mordont announced her intention to run for the post of leader of the Conservative Party and the prime minister of the country.
Before Truss was elected, Mordont also participated in the struggle for the premiership, but dropped out with 105 votes.
Johnson also decided to compete for the premiership.
As Sky News reported, he flew from the Dominican Republic to Britain in economy class with his family.
In addition, according to the channel, he received the support of more than 100 deputies.